PurposeMulti-shot diffusion-weighted EPI allows an increase in image resolution and reduced geometric distortions and can be combined with chemical-shift encoding (Dixon) to separate water/fat... Show morePurposeMulti-shot diffusion-weighted EPI allows an increase in image resolution and reduced geometric distortions and can be combined with chemical-shift encoding (Dixon) to separate water/fat signals. However, such approaches suffer from physiological motion-induced shot-to-shot phase variations. In this work, a structured low-rank-based navigator-free algorithm is proposed to address the challenge of simultaneously separating water/fat signals and correcting for physiological motion-induced shot-to-shot phase variations in multi-shot EPI-based diffusion-weighted MRI.Theory and MethodsWe propose an iterative, model-based reconstruction pipeline that applies structured low-rank regularization to estimate and eliminate the shot-to-shot phase variations in a data-driven way, while separating water/fat images. The algorithm is tested in different anatomies, including head–neck, knee, brain, and prostate. The performance is validated in simulations and in-vivo experiments in comparison to existing approaches.ResultsIn-vivo experiments and simulations demonstrated the effectiveness of the proposed algorithm compared to extra-navigated and an alternative self-navigation approach. The proposed algorithm demonstrates the capability to reconstruct in the multi-shot/Dixon hybrid space domain under-sampled datasets, using the same number of acquired EPI shots compared to conventional fat-suppression techniques but eliminating fat signals through chemical-shift encoding. In addition, partial Fourier reconstruction can also be achieved by using the concept of virtual conjugate coils in conjunction with the proposed algorithm.ConclusionThe proposed algorithm effectively eliminates the shot-to-shot phase variations and separates water/fat images, making it a promising solution for future DWI on different anatomies. Show less
Objective To implement magnetic resonance fingerprinting (MRF) on a permanent magnet 50 mT low-field system deployable as a future point-of-care (POC) unit and explore the quality of the parameter... Show moreObjective To implement magnetic resonance fingerprinting (MRF) on a permanent magnet 50 mT low-field system deployable as a future point-of-care (POC) unit and explore the quality of the parameter maps.Materials and methods 3D MRF was implemented on a custom-built Halbach array using a slab-selective spoiled steadystate free precession sequence with 3D Cartesian readout. Undersampled scans were acquired with different MRF flip angle patterns and reconstructed using matrix completion and matched to the simulated dictionary, taking excitation profile and coil ringing into account. MRF relaxation times were compared to that of inversion recovery ( IR) and multi-echo spin echo (MESE) experiments in phantom and in vivo. Furthermore, -B0 inhomogeneities were encoded in the MRF sequence using an alternating TE pattern, and the estimated map was used to correct for image distortions in the MRF images using a modelbased reconstruction.Results Phantom relaxation times measured with an optimized MRF sequence for low field were in better agreement with reference techniques than for a standard MRF sequence. In vivo muscle relaxation times measured with MRF were longer than those obtained with an IR sequence (T-1: 182 +/- 21.5 vs 168 +/- 9.89 ms) and with an MESE sequence (T-2: 69.8 +/- 19.7 vs 46.1 +/- 9.65 ms). In vivo lipid MRF relaxation times were also longer compared with IR (T-1: 165 +/- 15.1 ms vs 127 +/- 8.28 ms) and with MESE (T-2: 160 +/- 15.0 ms vs 124 +/- 4.27 ms). Integrated Delta B-0 estimation and correction resulted in parameter maps with reduced distortions.Discussion It is possible to measure volumetric relaxation times with MRF at 2.5 x 2.5 x 3.0 -mm(3) resolution in a 13 min scan time on a 50 mT permanent magnet system. The measured MRF relaxation times are longer compared to those measured with reference techniques, especially for T-2. This discrepancy can potentially be addressed by hardware, reconstruction and sequence design, but long-term reproducibility needs to be further improved. Show less
Purpose: To develop a method for MR Fingerprinting (MRF) sequence optimization that takes both the applied undersampling pattern and a realistic reference map into account. Methods: A predictive... Show morePurpose: To develop a method for MR Fingerprinting (MRF) sequence optimization that takes both the applied undersampling pattern and a realistic reference map into account. Methods: A predictive model for the undersampling error leveraging on perturbation theory was exploited to optimize the MRF flip angle sequence for improved robustness against undersampling artifacts. In this framework parameter maps from a previously acquired MRF scan were used as reference. Sequences were optimized for different sequence lengths, smoothness constraints and undersampling factors. Numerical simulations and in vivo measurements in eight healthy subjects were performed to assess the effect of the performed optimization. The optimized MRF sequences were compared to a conventionally shaped flip angle pattern and an optimized pattern based on the Cramer-Rao lower bound (CRB). Results: Numerical simulations and in vivo results demonstrate that the undersampling errors can be suppressed by flip angle optimization. Analysis of the in vivo results show that a sequence optimized for improved robustness against undersampling with a flip angle train of length 400 yielded significantly lower median absolute errors in T1: 5.6%+/- 2.9% and T2: 7.9%+/- 2.3% compared to the conventional (T1: 8.0%+/- 1.9%, T2: 14.5%+/- 2.6%) and CRB-based (T1: 21.6%+/- 4.1%, T2: 31.4%+/- 4.4%) sequences. Conclusion: The proposed method is able to optimize the MRF flip angle pattern such that significant mitigation of the artifacts from strong k-space undersampling in MRF is achieved. Show less
Nagtegaal, M.; Hartsema, E.; Koolstra, K.; Vos, F. 2022
Purpose To develop an efficient algorithm for multicomponent MR fingerprinting (MC-MRF) reconstructions directly from highly undersampled data without making prior assumptions about tissue... Show morePurpose To develop an efficient algorithm for multicomponent MR fingerprinting (MC-MRF) reconstructions directly from highly undersampled data without making prior assumptions about tissue relaxation times and expected number of tissues. Methods The proposed method reconstructs MC-MRF maps from highly undersampled data by iteratively applying a joint-sparsity constraint to the estimated tissue components. Intermediate component maps are obtained by a low-rank multicomponent alternating direction method of multipliers (MC-ADMM) including the non-negativity of tissue weights as an extra regularization term. Over iterations, the used dictionary compression is adjusted. The proposed method (k-SPIJN) is compared with a two-step approach in which image reconstruction and multicomponent estimations are performed sequentially and tested in numerical simulations and in vivo by applying different undersampling factors in eight healthy volunteers. In the latter case, fully sampled data serves as the reference. Results The proposed method shows improved precision and accuracy in simulations compared with a state-of-art sequential approach. Obtained in vivo magnetization fraction maps for different tissue types show reduced systematic errors and reduced noise-like effects. Root mean square errors in estimated magnetization fraction maps significantly reduce from 13.0%+/-$$ \pm $$ 5.8% with the conventional, two-step approach to 9.6%+/-$$ \pm $$ 3.9% and 9.6%+/-$$ \pm $$ 3.2% with the proposed MC-ADMM and k-SPIJN methods, respectively. Mean standard deviation in homogeneous white matter regions reduced significantly from 8.6% to 2.9% (two step vs. k-SPIJN). Conclusion The proposed MC-ADMM and k-SPIJN reconstruction methods estimate MC-MRF maps from highly undersampled data resulting in improved image quality compared with the existing method. Show less
Dong, Y.M.; Riedel, M.; Koolstra, K.; Osch, M.J.P. van; Börnert, P. 2022
The purpose of this study was to develop a self-navigation strategy to improve scan efficiency and image quality of water/fat-separated, diffusion-weighted multishot echo-planar imaging (ms-EPI).... Show moreThe purpose of this study was to develop a self-navigation strategy to improve scan efficiency and image quality of water/fat-separated, diffusion-weighted multishot echo-planar imaging (ms-EPI). This is accomplished by acquiring chemical shift-encoded diffusion-weighted data and using an appropriate water-fat and diffusion-encoded signal model to enable reconstruction directly from k-space data. Multishot EPI provides reduced geometric distortion and improved signal-to-noise ratio in diffusion-weighted imaging compared with single-shot approaches. Multishot acquisitions require corrections for physiological motion-induced shot-to-shot phase errors using either extra navigators or self-navigation principles. In addition, proper fat suppression is important, especially in regions with large B0 inhomogeneity. This makes the use of chemical shift encoding attractive. However, when combined with ms-EPI, shot-to-shot phase navigation can be challenging because of the spatial displacement of fat signals along the phase-encoding direction. In this work, a new model-based, self-navigated water/fat separation reconstruction algorithm is proposed. Experiments in legs and in the head–neck region of 10 subjects were performed to validate the algorithm. The results are compared with an image-based, two-dimensional (2D) navigated water/fat separation approach for ms-EPI and with a conventional fat saturation approach. Compared with the 2D navigated method, the use of self-navigation reduced the shot duration time by 30%–35%. The proposed algorithm provided improved diffusion-weighted water images in both leg and head–neck regions compared with the 2D navigator-based approach. The proposed algorithm also produced better fat suppression compared with the conventional fat saturation technique in the B0 inhomogeneous regions. In conclusion, the proposed self-navigated reconstruction algorithm can produce superior water-only diffusion-weighted EPI images with less artefacts compared with the existing methods. Show less
Koolstra, K.; Staring, M.; Bruin, P. de; Osch, M.J.P. van 2022
Background suppression (BGS) in arterial spin labeling (ASL) magnetic resonance imaging leads to a higher temporal signal-to-noise ratio (tSNR) of the perfusion images compared with ASL without BGS... Show moreBackground suppression (BGS) in arterial spin labeling (ASL) magnetic resonance imaging leads to a higher temporal signal-to-noise ratio (tSNR) of the perfusion images compared with ASL without BGS. The performance of the BGS, however, depends on the tissue relaxation times and on inhomogeneities of the scanner's magnetic fields, which differ between subjects and are unknown at the moment of scanning. Therefore, we developed a feedback loop (FBL) mechanism that optimizes the BGS for each subject in the scanner during acquisition. We implemented the FBL for 2D pseudo-continuous ASL scans with an echo-planar imaging readout. After each dynamic scan, the acquired ASL images were automatically sent to an external computer and processed with a Python processing tool. Inversion times were optimized on the fly using 80 iterations of the Nelder-Mead method, by minimizing the signal intensity in the label image while maximizing the signal intensity in the perfusion image. The performance of this method was first tested in a four-component phantom. The regularization parameter was then tuned in six healthy subjects (three males, three females, age 24-62 years) and set as lambda = 4 for all other experiments. The resulting ASL images, perfusion images, and tSNR maps obtained from the last 20 iterations of the FBL scan were compared with those obtained without BGS and with standard BGS in 12 healthy volunteers (five males, seven females, age 24-62 years) (including the six volunteers used for tuning of lambda). The FBL resulted in perfusion images with a statistically significantly higher tSNR (2.20) compared with standard BGS (1.96) ( p<5x10-3$$ p, two-sided paired t-test). Minimizing signal in the label image furthermore resulted in control images, from which approximate changes in perfusion signal can directly be appreciated. This could be relevant to ASL applications that require a high temporal resolution. Future work is needed to minimize the number of initial acquisitions during which the performance of BGS is reduced compared with standard BGS, and to extend the technique to 3D ASL. Show less
Purpose To learn a preconditioner that accelerates parallel imaging (PI) and compressed sensing (CS) reconstructions. Methods A convolutional neural network (CNN) with residual connections was used... Show morePurpose To learn a preconditioner that accelerates parallel imaging (PI) and compressed sensing (CS) reconstructions. Methods A convolutional neural network (CNN) with residual connections was used to train a preconditioning operator. Training and validation data were simulated using 50% brain images and 50% white Gaussian noise images. Each multichannel training example contains a simulated sampling mask, complex coil sensitivity maps, and two regularization parameter maps. The trained model was integrated in the preconditioned conjugate gradient (PCG) method as part of the split Bregman CS method. The acceleration performance was compared with that of a circulant PI-CS preconditioner for varying undersampling factors, number of coil elements and anatomies. Results The learned preconditioner reduces the number of PCG iterations by a factor of 4, yielding a similar acceleration as an efficient circulant preconditioner. The method generalizes well to different sampling schemes, coil configurations and anatomies. Conclusion It is possible to learn adaptable preconditioners for PI and CS reconstructions that meet the performance of state-of-the-art preconditioners. Further acceleration could be achieved by optimizing the network architecture and the training set. Such a preconditioner could also be integrated in fully learned reconstruction methods to accelerate the training process of unrolled networks. Show less
Objective To visualize the encoding capability of magnetic resonance fingerprinting (MRF) dictionaries. Materials and methods High-dimensional MRF dictionaries were simulated and embedded into a... Show moreObjective To visualize the encoding capability of magnetic resonance fingerprinting (MRF) dictionaries. Materials and methods High-dimensional MRF dictionaries were simulated and embedded into a lower-dimensional space using t-distributed stochastic neighbor embedding (t-SNE). The embeddings were visualized via colors as a surrogate for location in low-dimensional space. First, we illustrate this technique on three different MRF sequences. We then compare the resulting embeddings and the color-coded dictionary maps to these obtained with a singular value decomposition (SVD) dimensionality reduction technique. We validate the t-SNE approach with measures based on existing quantitative measures of encoding capability using the Euclidean distance. Finally, we use t-SNE to visualize MRF sequences resulting from an MRF sequence optimization algorithm. Results t-SNE was able to show clear differences between the color-coded dictionary maps of three MRF sequences. SVD showed smaller differences between different sequences. These findings were confirmed by quantitative measures of encoding. t-SNE was also able to visualize differences in encoding capability between subsequent iterations of an MRF sequence optimization algorithm. Discussion This visualization approach enables comparison of the encoding capability of different MRF sequences. This technique can be used as a confirmation tool in MRF sequence optimization. Show less
Dong, Y.M.; Koolstra, K.; Riedel, M.; Osch, M.J.P. van; Bornert, P. 2021
Purpose To develop a new water-fat separation and B-0 estimation algorithm to effectively suppress the multiple resonances of fat signal in EPI. This is especially relevant for DWI where fat is... Show morePurpose To develop a new water-fat separation and B-0 estimation algorithm to effectively suppress the multiple resonances of fat signal in EPI. This is especially relevant for DWI where fat is often a confounding factor. Methods Water-fat separation based on chemical-shift encoding enables robust fat suppression in routine MRI. However, for EPI the different chemical-shift displacements of the multiple fat resonances along the phase-encoding direction can be problematic for conventional separation algorithms. This work proposes a suitable model approximation for EPI under B-0 and fat off-resonance effects, providing a feasible multi-peak water-fat separation algorithm. Simulations were performed to validate the algorithm. In vivo validation was performed in 6 volunteers, acquiring spin-echo EPI images in the leg (B-0 homogeneous) and head-neck (B-0 inhomogeneous) regions, using a TE-shifted interleaved EPI sequence with/without diffusion sensitization. The results are numerically and statistically compared with voxel-independent water-fat separation and fat saturation techniques to demonstrate the performance of the proposed algorithm. Results The reference separation algorithm without the proposed spatial shift correction caused water-fat ambiguities in simulations and in vivo experiments. Some spectrally selective fat saturation approaches also failed to suppress fat in regions with severe B-0 inhomogeneities. The proposed algorithm was able to achieve improved fat suppression for DWI data and ADC maps in the head-neck and leg regions. Conclusion The proposed algorithm shows improved suppression of the multi-peak fat components in multi-shot interleaved EPI applications compared to the conventional fat saturation approaches and separation algorithms. Show less
Koolstra, K.; O'Reilly, T.; Bornert, P.; Webb, A. 2021
Objective To correct for image distortions produced by standard Fourier reconstruction techniques on low field permanent magnet MRI systems with strong B-0 inhomogeneity and gradient field... Show moreObjective To correct for image distortions produced by standard Fourier reconstruction techniques on low field permanent magnet MRI systems with strong B-0 inhomogeneity and gradient field nonlinearities. Materials and methods Conventional image distortion correction algorithms require accurate Delta B-0 maps which are not possible to acquire directly when the B-0 inhomogeneities also produce significant image distortions. Here we use a readout gradient time-shift in a TSE sequence to encode the B-0 field inhomogeneities in the k-space signals. Using a non-shifted and a shifted acquisition as input, Delta B-0 maps and images were reconstructed in an iterative manner. In each iteration, Delta B-0 maps were reconstructed from the phase difference using Tikhonov regularization, while images were reconstructed using either conjugate phase reconstruction (CPR) or model-based (MB) image reconstruction, taking the reconstructed field map into account. MB reconstructions were, furthermore, combined with compressed sensing (CS) to show the flexibility of this approach towards undersampling. These methods were compared to the standard fast Fourier transform (FFT) image reconstruction approach in simulations and measurements. Distortions due to gradient nonlinearities were corrected in CPR and MB using simulated gradient maps. Results Simulation results show that for moderate field inhomogeneities and gradient nonlinearities, Delta B-0 maps and images reconstructed using iterative CPR result in comparable quality to that for iterative MB reconstructions. However, for stronger inhomogeneities, iterative MB reconstruction outperforms iterative CPR in terms of signal intensity correction. Combining MB with CS, similar image and Delta B-0 map quality can be obtained without a scan time penalty. These findings were confirmed by experimental results. Discussion In case of B-0 inhomogeneities in the order of kHz, iterative MB reconstructions can help to improve both image quality and Delta B-0 map estimation. Show less
Purpose To design a low-cost, portable permanent magnet-based MRI system capable of obtaining in vivo MR images within a reasonable scan time. Methods A discretized Halbach permanent magnet array... Show morePurpose To design a low-cost, portable permanent magnet-based MRI system capable of obtaining in vivo MR images within a reasonable scan time. Methods A discretized Halbach permanent magnet array with a clear bore diameter of 27 cm was designed for operation at 50 mT. Custom-built gradient coils, RF coil, gradient amplifiers, and RF amplifier were integrated and tested on both phantoms and in vivo. Results Phantom results showed that the gradient nonlinearity in the y-direction and z-direction was less than 5% over a 15-cm FOV and did not need correcting. For the x-direction, it was significantly greater, but could be partially corrected in postprocessing. Three-dimensional in vivo scans of the brain of a healthy volunteer using a turbo spin-echo sequence were acquired at a spatial resolution of 4 x 4 x 4 mm in a time of about 2 minutes. The T-1-weighted and T-2-weighted scans showed a good degree of tissue contrast. In addition, in vivo scans of the knee of a healthy volunteer were acquired at a spatial resolution of about 3 x 2 x 2 mm within 12 minutes to show the applicability of the system to extremity imaging. Conclusion This work has shown that it is possible to construct a low-field MRI unit with hardware components costing less than 10 000 Euros, which is able to acquire human images in vivo within a reasonable data-acquisition time. The system has a high degree of portability with magnet weight of approximately 75 kg, gradient and RF amplifiers each 15 kg, gradient coils 10 kg, and spectrometer 5 kg. Show less
The aim of this thesis was to develop fast reconstruction and acquisition techniques for MRI that can support clinical applications where time is a limiting factor. In general, fast acquisition... Show moreThe aim of this thesis was to develop fast reconstruction and acquisition techniques for MRI that can support clinical applications where time is a limiting factor. In general, fast acquisition techniques were realized by undersampling k-space, while fast reconstruction techniques were achieved by using efficient numerical algorithms. In particular, undersampled acquisitions were processed in a CS and MRF framework. Preconditioning techniques were used to accelerate CS reconstructions, and a number of challenges encountered in MRF were addressed using appropriate post-processing techniques. Show less
Quantitative MRI methods that estimate multiple physical parameters simultaneously often require the fitting of a computational complex signal model defined through the Bloch equations. Repeated... Show moreQuantitative MRI methods that estimate multiple physical parameters simultaneously often require the fitting of a computational complex signal model defined through the Bloch equations. Repeated Bloch simulations can be avoided by matching the measured signal with a precomputed signal dictionary on a discrete parameter grid (i.e. lookup table) as used in MR Fingerprinting. However, accurate estimation requires discretizing each parameter with a high resolution and consequently high computational and memory costs for dictionary generation, storage, and matching. Here, we reduce the required parameter resolution by approximating the signal between grid points through B-spline interpolation. The interpolant and its gradient are evaluated efficiently which enables a least-squares fitting method for parameter mapping. The resolution of each parameter was minimized while obtaining a user-specified interpolation accuracy. The method was evaluated by phantom and in-vivo experiments using fully-sampled and undersampled unbalanced (FISP) MR fingerprinting acquisitions. Bloch simulations incorporated relaxation effects (T-1, T-2), proton density (PD), receiver phase ( phi(0)), transmit field inhomogeneity (B-1(+)), and slice profile. Parametermapswere comparedwith those obtained from dictionary matching, where the parameter resolution was chosen to obtain similar signal (interpolation) accuracy. For both the phantom and the in-vivo acquisition, the proposed method approximated the parameter maps obtained through dictionary matching while reducing the parameter resolution in each dimension (T-1, T-2, B-1(+)) by - on average - an order of magnitude. In effect, the applied dictionary was reduced from 1.47GB to 464KB. Furthermore, the proposed method was equally robust against undersampling artifacts as dictionarymatching. Dictionary fittingwith B-spline interpolation reduces the computational and memory costs of dictionary-based methods and is therefore a promising method for multi- parametric mapping. Show less
Purpose To minimize the known biases introduced by fat in rapid T-1 and T-2 quantification in muscle using a single-run magnetic resonance fingerprinting (MRF) water-fat separation sequence.... Show morePurpose To minimize the known biases introduced by fat in rapid T-1 and T-2 quantification in muscle using a single-run magnetic resonance fingerprinting (MRF) water-fat separation sequence. Methods The single-run MRF acquisition uses an alternating in-phase/out-of-phase TE pattern to achieve water-fat separation based on a 2-point DIXON method. Conjugate phase reconstruction and fat deblurring were applied to correct for B-0 inhomogeneities and chemical shift blurring. Water and fat signals were matched to the on-resonance MRF dictionary. The method was first tested in a multicompartment phantom. To test whether the approach is capable of measuring small in vivo dynamic changes in relaxation times, experiments were run in 9 healthy volunteers; parameter values were compared with and without water-fat separation during muscle recovery after plantar flexion exercise. Results Phantom results show the robustness of the water-fat resolving MRF approach to undersampling. Parameter maps in volunteers show a significant (P < .01) increase in T-1 (105 +/- 94 ms) and decrease in T-2 (14 +/- 6 ms) when using water-fat-separated MRF, suggesting improved parameter quantification by reducing the well-known biases introduced by fat. Exercise results showed smooth T-1 and T-2 recovery curves. Conclusion Water-fat separation using conjugate phase reconstruction is possible within a single-run MRF scan. This technique can be used to rapidly map relaxation times in studies requiring dynamic scanning, in which the presence of fat is problematic. Show less
Purpose: To explore the feasibility of MR Fingerprinting (MRF) to rapidly quantify relaxation times in the human eye at 7T, and to provide a data acquisition and processing framework for future... Show morePurpose: To explore the feasibility of MR Fingerprinting (MRF) to rapidly quantify relaxation times in the human eye at 7T, and to provide a data acquisition and processing framework for future tissue characterization in eye tumor patients.Methods: In this single-element receive coil MRF approach with Cartesian sampling, undersampling is used to shorten scan time and, therefore, to reduce the degree of motion artifacts. For reconstruction, approaches based on compressed sensing (CS) and matrix completion (MC) were used, while their effects on the quality of the MRF parameter maps were studied in simulations and experiments. Average relaxation times in the eye were measured in 6 healthy volunteers. One uveal melanoma patient was included to show the feasibility of MRF in a clinical context.Results: Simulation results showed that an MC-based reconstruction enables large undersampling factors and also results in more accurate parameter maps compared with using CS. Experiments in 6 healthy volunteers used a reduction in scan time from 7:02 to 1:16 min,producing images without visible loss of detail in the parameter maps when using the MC-based reconstruction. Relaxation times from 6 healthy volunteers are in agreement with values obtained from fully sampled scans and values in literature, and parameter maps in a uveal melanoma patient show clear difference in relaxation times between tumor and healthy tissue.Conclusion: Cartesian-based MRF is feasible in the eye at 7T. High undersampling factors can be achieved by means of MC, significantly shortening scan time and increasing patient comfort, while also mitigating the risk of motion artifacts. Show less
Koolstra, K.; Gemert, J. van; Bornert, P.; Webb, A.; Remis, R. 2019
Purpose: Design of a preconditioner for fast and efficient parallel imaging (PI) and compressed sensing (CS) reconstructions for Cartesian trajectories.Theory: PI and CS reconstructions become time... Show morePurpose: Design of a preconditioner for fast and efficient parallel imaging (PI) and compressed sensing (CS) reconstructions for Cartesian trajectories.Theory: PI and CS reconstructions become time consuming when the problem size or the number of coils is large, due to the large linear system of equations that has to be solved in l(1) and l(2)-norm based reconstruction algorithms. Such linear systems can be solved efficiently using effective preconditioning techniques.Methods: In this article we construct such a preconditioner by approximating the system matrix of the linear system, which comprises the data fidelity and includes total variation and wavelet regularization, by a matrix that is block circulant with circulant blocks. Due to this structure, the preconditioner can be constructed quickly and its inverse can be evaluated fast using only two fast Fourier transformations. We test the performance of the preconditioner for the conjugate gradient method as the linear solver, integrated into the well-established Split Bregman algorithm.Results: The designed circulant preconditioner reduces the number of iterations required in the conjugate gradient method by almost a factor of 5. The speed up results in a total acceleration factor of approximately 2.5 for the entire reconstruction algorithm when implemented in MATLAB, while the initialization time of the pre-conditioner is negligible.Conclusion: The proposed preconditioner reduces the reconstruction time for PI and CS in a Split Bregman implementation without compromising reconstruction stability and can easily handle large systems since it is Fourier-based, allowing for efficient computations. Show less
Jaarsma-Coes, M.; Vught, L. van; Koolstra, K.; Beenakker, J.W.B. 2018
